SELECTED WORKING PAPERS

Qiao, Y., Zhang, J., Zhu, W., Wang, C.-W. (2024). Quantile-based Interpretable Neural Network Models: Mortality Forecasting and Actuarial Simulations. R&R. Insurance: Mathematics and Economics. [PDF].

This paper introduces a class of quantile-based, interpretable neural network (NN) mod- els for mortality prediction: the Lee-Carter neural network (LCNN) model, the Renshaw- Haberman neural network (RHNN) model, and the simple neural network (simpleNN) model that balances simplicity with predictive performance. These models preserve the linear interpretability of classic stochastic mortality models while harnessing the flexibility of NNs to capture complex nonlinear patterns in mortality data, thereby achieving enhanced predictive performance. Leveraging a composite loss function that integrates pinball, me- dian anchoring, and quantile-crossing penalty terms, we estimate mortality quantiles and develop an efficient simulation scheme based on interpolation. This framework provides distributional insights essential for pricing, reserving and risk management. Extensive em- pirical analyses across multiple populations demonstrate that the proposed models consis- tently outperform traditional approaches in predictive accuracy. We further illustrate their practical utility through an application to longevity swap pricing.

Keywords:  Interpretable Neural Network, Mortality Prediction, Longevity Risk, Stochastic Mortality Model, Quantile Regression, Monte Carlo Simulation, Longevity Swap

Xu, Y.*, Tan, K. S., Pan, G, Porth, L., and Zhu, W. (2021). Sustainable Area-Yield Insurance Program with Optimal Risk Pooling: A Behavior-Based Machine Learning Approach. [SSRN], [PDF].

Area-yield insurance offers a sustainable alternative to traditional individual-loss programs by reducing moral hazard, administrative costs, and data requirements, but its efficiency is often limited by basis risk. This paper proposes a behavior- based machine learning approach to optimally form risk pools, improving contract performance. We first determine the optimal number of risk pools through farmers’ behaviour under a utility maximization framework, then apply unsupervised spectral clustering to group farmers with similar risk histories. This framework enhances the efficiency of the area-yield insurance contract and addresses challenges of high- dimensionality and computational complexity. Using corn and soybean production at both county- and farm-level in the U.S. Heartland, we show that our method significantly reduces basis risk and farmers’ tail risk, with potential profit gains of up to $2.8 billion for corn production.

Keywords:  Sustainability, Area yield, Basis risk, Crop insurance, Machine learning.

Xu, Y.*, Tan, K. S., and Zhu, W. (2022). A Geo-Hierarchical Deep Learning Approach for Flood Insurance Modeling and Pricing. [SSRN], [PDF] (Previously titled "Borrowing Information Across Space and Time: Pricing Flood Risk with Physics-based Hierarchical Machine Learning Models")

Flood risk is an increasingly urgent concern as climate change intensifies the frequency and severity of extreme events. Flood insurance is a key tool to protect against such risk, but its modeling and pricing remain challenging. This paper proposes a Geo-Hierarchical Deep Learning (GHDL) framework, a scalable, interpretable, and cost-efficient approach, to generate high-resolution flood hazard factors and inform insurance pricing. The GHDL framework can effectively capture spatial dependencies that are essential for an accurate flood risk assessment by incorporating geographical connectivity directly into deep learning models. Using data from the Mississippi River Basin, we show that GHDL achieves 86%–91% accuracy in extreme scenarios, outperforming climate-uninformed and benchmark deep learning models. Applied to the National Flood Insurance Program (NFIP), GHDL-derived hazard factors reduce net premiums by 33.5% and solvency capital requirements by 32.3%. These improvements enhance pricing adequacy and contribute to the long-term sustainability of public flood insurance programs.

Keywords:  Flood risk, Climate risk, Deep learning, Ratemaking, Colvency capital requirement.

Feng, Q., Jaidee, S.**, Pan, G., and Zhu, W. (2022). Robust Testing in High-Dimensional Linear Model, Working Paper. 

We propose a joint significance of many coefficients in high-dimensional linear regression that is robust to unconditional heteroskedasticity and autocorrelation of unknown form within regression errors. Exploiting information on the limiting behaviors of an equally weighted empirical spectral distribution with its weighted counterpart, we derive the asymptotic property of proposed statistics without a priori knowledge of the sparsity level of tested parameters and the underlying structure of regression errors. Instead, we adopt the Random Matrix Theory and self-normalization technique to comprehend the curse of dimensionality, heteroskedasticity, and autocorrelation simultaneously. Thanks to the naturality of parametric framework, the limiting Gaussian distribution of our proposed statistics are free from the choice of kernel functions and bandwidth selections. Simulation studies confirm the accuracy of type-I error with satisfactory empirical testing power in a finite sample over many different types of dependent data such as time-series data and spatially dependent data. In practice, to avoid an upward size distortion from using conventional statistics, we recommend practitioners take the curse of dimensionality into account when the intensity ratio is greater than 0.05.